1957 AHSME Problems/Problem 2

Problem

In the equation $2x^2 - hx + 2k = 0$ , the sum of the roots is $4$ and the product of the roots is $-3$ . Then $h$ and $k$ have the values, respectively:

$\textbf{(A)}\ 8\text{ and }{-6} \qquad \textbf{(B)}\ 4\text{ and }{-3}\qquad \textbf{(C)}\ {-3}\text{ and }4\qquad \textbf{(D)}\ {-3}\text{ and }8\qquad \textbf{(E)}\ 8\text{ and }{-3}$

Solution

Let the roots of the given equation be $r$ and $s$ . Then, by Vieta's Formulas, we have the following: \begin{align*} \frac{h}{2} = r+s = 4 &\rightarrow h = 8 \\ \frac{2k}{2} = rs = -3 &\rightarrow k = -3 \\ \end{align*}

Thus, our answer is $\boxed{\textbf{(E) } 8 \text{ and } 3}$ .

1957 AHSC (Problems • Answer Key • Resources)
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1957 AHSME Problems/Problem 2

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